old age vs autumn years

old age and autumn years both are nouns.

Word	Noun	Adjective	Verb	Adverb
old age	Yes	No	No	No
autumn years	Yes	No	No	No

As nouns, autumn years is a hyponym of old age; that is, autumn years is a word with a more specific, narrower meaning than old age:

old age: a late time of life
autumn years: (literary) the later years of one's life, especially after one has finished their career.

Other hyponyms of old age include dotage, second childhood, senility, decrepitude.

old age (noun)	autumn years (noun)
a late time of life	(literary) the later years of one's life, especially after one has finished their career.